Answer:
The equation of the line is [tex]y = \frac{2x}{3} - 2[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Parallel lines:
When two lines are parallel, they have the same slope.
Finding the slope:
When we have two points on a line, the slope is given by the change in y divided by the change in x.
In this question, we have these following points: (0,-1) and (3,1)
Change in y: 1 - (-1) = 1 + 1 = 2
Change in x: 3 - 0 = 3
Slope: [tex]m = \frac{2}{3}[/tex]
The equation of the line has the following format:
[tex]y = \frac{2x}{3} + b[/tex]
x-intercept of 3
This means that when [tex]y = 0, x = 3[/tex]. We use this to find b. So
[tex]y = \frac{2x}{3} + b[/tex]
[tex]0 = \frac{2*3}{3} + b[/tex]
[tex]0 = 2 + b[/tex]
[tex]b = -2[/tex]
So
[tex]y = \frac{2x}{3} - 2[/tex]
